ARFIMA模型参数估计方法比较及在金融时间序列的应用

发布时间：2018-04-14 11:06

本文选题：长程相关性 + ARFIMA模型　；参考：《湘潭大学》2017年硕士论文

【摘要】：长记忆性是对序列高阶相关结构的一种描述,又称长期相关性。具有长记忆性的序列在相距甚远两个观察值之间有某种稳定的依存关系,衰减缓慢的自相关函数。金融时间序列的分形结构、肥尾分布、长期记忆等非线性特征,都是当今最受关注的研究课题之一。为深入了解并研究经济时间序列所呈现出长记忆性特征,本文重点研究了能刻画长记忆性的分整移动自回归模型(ARFIMA)模型,介绍了有关长记忆时间序列的概念、检验及建模等内容。本文应用ADF、PP和KPSS三种方法来检验上证指数和深证成指两条序列的平稳性,并用经典的R/S分析法和修正的R/S分析法以及V/S分析法来分析两条序列的长记忆性。结论显示一致支持上证和深证的日收益序列都有长记忆性,而且上证序列的长记忆性比深证的强。基于长记忆性的检验结果,本文对两条序列采用B-J方法进行ARFIMA建模。通过信息准则比较确定为,ARFIMA(6, d,2)是描述上证日收益序列长记忆性最合适的模型,ARFIMA(5, d,2)是描述深证成指日收益序列长记忆性最合适的模型。通过实证研究得出,中国股市中确实存在长记忆性,但中国股市缺乏有效性。
[Abstract]:Long memory is a description of high-order correlation structure in sequence, which is also called long-term correlation.The sequence with long memory has some stable dependence between the two observation values and the autocorrelation function with slow decay.The fractal structure, fat tail distribution, long-term memory and other nonlinear characteristics of financial time series are one of the most concerned research topics.In order to deeply understand and study the long memory characteristics of economic time series, this paper focuses on the integral moving autoregressive model (ARFIMA), which can depict long memory, and introduces the concept of long memory time series.Inspection and modeling.In this paper, three methods, ADFP-PP and KPSS, are used to test the smoothness of the two sequences, and the classical R / S analysis, the modified R / S analysis and the V / S analysis are used to analyze the long memory properties of the two sequences.The results show that the daily earnings sequences of both Shanghai and Shenzhen have long memory, and the long memory of Shanghai is stronger than that of Shenzhen.Based on the test results of long memory, B-J method is used to model two sequences in this paper.Through the comparison of information criteria, it is determined that ARFIMA6, dan2) is the most suitable model to describe the long memory of the daily earnings sequence of Shanghai Stock Exchange. It is the most appropriate model to describe the long memory property of the daily earnings sequence of Shenzhen Stock Exchange.The empirical study shows that there is a long memory in Chinese stock market, but it lacks efficiency.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F832.51

【参考文献】